of 11
Reviewers' comments:
Reviewer #1 (Remarks to the Author):
In the manuscript "Mechanical On
-
Chip Microwave Circulator”, the authors have reported the
experimental realization of frequency tunable microwave isolator/circulator. The experiment is
indeed very interesting and the data well understood and modeled in de
tail. It would generate a
lot of excitement, as an on
-
chip microwave isolator/circulator which could even work at the single
“photon” level. In my opinion, the manuscript is suitable for publication in Nature Communication,
after the authors have addressed
the following comments and questions:
1
Can the authors discuss more details about the advantages of such devices, especially for the
quantum information processing? The discussion in the manuscript is too simple. It will be really
helpful if the author
s can estimate some parameters for experiment, i.e. temperature,
cooperativity.
.
2. What’s the bandwidth of the isolator/circulator? Is there any more application of such small
bandwidth especially for the microwave system?
3. What’s the input power t
o drive the mechanics and get higher cooperativity? Is there any
nonlinear effect?
4. The figures are small and illegible to read. It can be improved to one row. And what’s the unit of
the Fig.2b & 3b?
Reviewer #2 (Remarks to the Author):
In the ma
nuscript “Mechanical On
-
Chip Microwave Circulator” the authors report on an experiment
based on the existing theoretical ideas, to implement a microwave isolator/circulator. Integrating
optomechanics with superconducting qubits, by using the same microwave
technology, is
interesting and could provide new possibilities. This work builds on the existing ideas and
experiments in cavity optomechanics (see ref. 26 and refs within). The authors demonstrate that
not only the operating frequency of the device can b
e tuned, but also the direction of the
isolation/circulation can be controlled. The experimental results are in a good agreement with
authors’ theoretical analysis. I think if the authors address the issues below, publishing the paper
in Nature communicati
on can benefit a wide range of audience.
1) In the second paragraph, where limitations of the existing circulators based on magneto
-
optic
effects have been discussed, no reference is presented.
2) I think it helps if the authors clarify what the opt
omechanical and electromechanical couplings
refer to in their setup.
3) While the physics of non
-
reciprocity is based on reservoir engineering and the presence of
mechanical loss, the intuitive picture behind non
-reciprocal mechanism is postponed after
the
presentation of formalism and the results. I think it’s helpful to present the physical picture first,
and then delve into a mathematical description.
4) It seems that in insets of Fig 3b the black arrow indicates the circulation direction. It would
be
useful to mention it in the caption.
Reviewer #3 (Remarks to the Author):
The primary innovation in the paper "Mechanical On-Chip Microwave Circulator" is the first
experimental electro-mechanical circulator that is potentially chip-compatible with other cryogenic
microwave components. This is in contrast to the various demonstrations of opto- (refs 24-26) and
electro-mechanical (refs 28 & 29, apparently 29 is now in print) _isolators_, which are two port
non-reciprocal devices, as opposed to three.
Not without good reason, non-reciprocal components are having a bit of a "moment" right now in
integrated micro- and quantum-devices in the optical and RF domains, due to the limitations of the
standard technologies based on permanent magnets, as mentioned in the manuscript. Thus, this
paper opens the door to a new technological approach (i.e. mechanical) to achieving non-
reciprocity, and has the potential to be of interest to a fairly wide audience in integrated micro-
and quantum-devices in the optical and RF domains. So I feel the topic matter and this paper in
general deserves to be published in a broad journal. The main limitation of the paper is that the
circulator's performance is extremely poor by almost every metric compared to already proven
Joseph junction-based RF circulators (refs. 4 & 5 are two, but not the only examples), and it's not
at all clear how the mechanical approach could ever out compete them. So, it deserves publication
for its basic science, even if I am very pessimistic about its technological impact.
Assuming the authors can adequately address my questions and comments further below, I would
generally support publication in Nature Communications.
1) A small thing, but I generally prefer to describe devices such as this one as "electro-mechanics"
not "opto-mechanics." Here the authors sort of use the terms interchangeably, which is not
uncommon in the field because they are so closely linked, but I wonder if it might prove confusing
to other readers.
2) Fig. 1c needs to be redrawn to make the electrical connectivity much clearer. I cannot tell at all
what is electrically connected to what in the nanowire device and the text didn't help me
understand what I couldn't see in the figure. In particular, I cannot tell at all where the Vdc is
applying its potential. I am very confused why "As expected, resonators 1 and 3 are tuned to
higher frequency due to an increased vacuum gap while resonator 2 is tuned to lower frequency."
As far as I can tell in Fig. 1c, resonators 2 & 3 look identical.
3) In figure 1a, it looks like there are two additional inductively coupled ports. What are these for?
4) Please state the overall footprint area of the device.
5) If the cooperativity employed in the main text figures was stated, I missed it. Similarly, Please
also state the pump power required to achieve this cooperativity in dBm. This required power
metric is helpful in comparing this technology to others, such as the JJ devices.
6) What is the relationship between the theory discussed at length in this paper to that described
in the theory papers referenced in refs 6, 22, & 23? What is the relationship between the theory in
this paper and the theory in the JJ-based components? For example, ref. 4 also involves
parametric frequency conversion between the three port modes and two internal modes to achieve
circulation. Is this approach and that one formally equivalent?
7) I want to see not just the forward and backward scattering matrix elements, but S11, S22, &
S33 as well. These input reflections are as important as the isolation for a usable device.
8) Similarly, I want to see an output PSD of all three ports while the component is circulating.
Again, as a practical matter, S
-parameters are not the only thing you care about in a c
irculator,
_especially_ an active one. This device employs six pump tones that are orders of magnitude
stronger than the signal tones and merely MHzs from the signal carriers. It is critically important to
know how bad all this RF leakage is.
9) I think
it would benefit readers if the authors provided more of an honest assessment of this
technology vis a vis other non
-
magnetic approaches. In particular, the JJ devices seems to out
perform this one in just about every way, and it's not at all clear if this
could ever change. For
example, this device provided ~10 dB relative isolation over merely ~300 Hz, while ref. 4 (the first
ever demonstration) had the same over 11 MHz. This component may be tuned by 30 MHz, while
that one could be tuned up to 400 MHz. T
his one had ~4 quanta of added noise, while that one
had 0.5 (quantum limited). This one requires six RF pumps, that one 3. Presumably the pump
power required here is again orders of magnitude greater than in ref. 4, because the nonlinearity
is so much wea
ker. If I had to guess, this mechanical technology might only be able to outperform
the JJ ones in 1 dB compression point, again because the nonlinearity is so much weaker.
As for the proposed application of superconducting qubit readout, the bandwidth o
f those signals
are measured in MHz, and carriers can easily vary by 100 MHz without a very well controlled
process. Even with its better parameters, the limitations of ref. 4 have yielded little actual
technological impact so far for this application eith
er. I want to reiterate that publishable work just
has to be innovative, rather than technologically competitive, but the authors can only help the
field by comparing it to other technologies and offering more guidance on where improvements will
be best ma
de.
We thank the referee for this positive comment about publication of our manuscript in Nature
communication.
1a
Can
the authors discuss more details about the advantages of such devices, especially for the
quantum
information processing? The discussion in the manuscript is too simple.
We have
added a more detailed description of the purpose of a microwave circulator for quantum
information
processing in the first paragraph of the introduction.
We have
also added the main advantages of a mechanical realization of a microwave circulator, in
parti
cular with respect to Josephson junction devices in the conclusion of the main text.
1.b
It will be really helpful if the authors can estimate some parameters for experiment, i.e. temperature,
cooperati
vity.
We thank
the referee for raising this point. In the main text we added the measured refrigerator
temperature
of 10 mK, the measured thermalization temperature of the mechanical modes of (18 / 25) mK
corresp
onding to a thermal phonon number of (85 / 90) for the mechanical modes 1 and 2. We also report
the sing
le cavity, single mechanical mode cooperativities for the pump powers used in the presented
isolator a
nd circulator experiments.
2a. What’s
the bandwidth of the isolator/circulator?
The
instantaneous bandwidth of the device is a combination of the effective mechanical damping rates
Γ
,
as defin
ed in the equation C14 of the appendix. In our experiment they are given as
Γ
,
=2
190
Hz and
Γ
,
=2
407
Hz
for the isolator and
Γ
,
=2
209
.9
Hz
and
Γ
,
=2
624
.9
Hz
for the
circulato
r. The bandwidth of the system is given by
=
,
,
,
,
(see R
ef [34] of the manuscript).
This
results in a total bandwidth of ~ 518 Hz for the isolator and ~ 628 Hz for the circulator in agreement
with the
results presented in figures 2 and 3.
2b. Is the
re any more application of such small bandwidth especially for the microwave system?
Narrow
bandwidth signal processing devices, such as the one presented, may still be used for example for
narrow
-band tunable filters and switches for effective noise rejection and sensitive precision
measur
ements. On the other hand, we would like to point out that the shown bandwidth is not yet
funda
mentally limited at this point. It is a first proof of principle device. In fact, spurious mechanical
modes
prevented us to broaden the mechanics more using higher pump powers. Further design changes
should
improve the bandwidth to a level where it becomes more useful for circuit QED applications.
3. Wh
at’s the input power to drive the mechanics and get higher cooperativity? Is there any nonlinear
effect?
We have added the applied powers at the device inputs in the main text together with the cooperativities.
In principle we would be able to apply up to about 10 dB higher powers before we observe nonlinear
effects. This would greatly improve the bandwidth of the wavelength conversion and the isolator (using
the 3
rd
cavity as a dissipative bath). However, the device showed additional weakly coupled mechanical
In the manuscript "Mechanica
l On-Chip Microwave
Circula
tor” , the authors have reported the
experimental realization of frequency tunable microwave isolator/circulator. The experiment is indeed
very interesting and the data well understood and modeled in detail. It would generate a lot o
f excitement,
as an on-chip
micro
wave isolator/circulator
which could even work at
the single “photon”
level. In
my
opinion,
the manuscrip
t is suitable
for publicat
ion in Nature
Communication, after
the authors have
addres
sed the following comments and
questions:
Reviewer #1 (Remarks to the Author):
m
odes in the vicinity of the main modes whose origin is not entirely clear (potentially mixing with out of
plane membrane modes). These additional modes make the interpretation of the measurement data very
difficult so we chose to work at lower power.
4.
The figures are small and illegible to read. It can be improved to one row. And what’s the unit of the
Fig. 2b
& 3b?
We have increase the figure sizes and added the missing labels as recommended.
Re
viewer #2 (Remarks to the Author):
In
the manuscript “Mechanical On-Chip Microwave Circulator” the authors report on an experiment
bas
ed on the existing theoretical ideas, to implement a microwave isolator/circulator. Integrating
opt
omechanics with superconducting qubits, by using the same microwave technology, is interesting and
coul
d provide new possibilities. This work builds on the existing ideas and experiments in cavity
opt
omechanics (see ref. 26 and refs within). The authors demonstrate that not only the operating
fre
quency of the device can be tuned, but also the direction of the isolation/circulation can be controlled.
Th
e experimental results are in a good agreement with authors’ theoretical analysis. I think if the authors
addres
s the issues below, publishing the paper in Nature communication can benefit a wide range of
audi
ence.
We thank referee for these positive comments.
1)
In the second paragraph, where limitations of the existing circulators based on magneto-optic effe
cts
have
been discussed, no reference is presented.
We have added two references [13][14] outlining the functionality and magnetic field requirements of
ferrite based commercial circulators and revised the text to highlight current limitations of commercial
circulators.
2)
I think it helps if the authors clarify what the optomechanical and electromechanical couplings refer to
in
their setup.
We thank the referee for pointing this out. We have been using the terms optomechanial and
electromechanical coupling interchangeably. In order to avoid any confusion we now only use the term
electromechanical coupling in the manuscript. The electromechanical coupling between a single
microwave resonator
i
and mechanical oscillator
j
is defined in the paragraph containing equation 1 of the
main text as
=
,
w
ith
t
he number of drive photons in the system. Section 1 of the SI
outlines the definition and calibrated values of the vacuum field electromechanical coupling
,
.
3)
While the physics of non-reciprocity is based on reservoir engineering and the presence of mechanical
los
s, the intuitive picture behind non-reciprocal mechanism is postponed after the presentation of
forma
lism and the results. I think it’s helpful to present the physical picture first, and then delve into a
ma
thematical description.
As suggested we have added an intuitive explanation for the origin of nonre
ciprocity right before going
in
to the theoretical details.
We also revised the main text and now present the intuitive picture about the
bandwidth of
the isolator
before presenting the results in the second paragraph of page 4.
4) It seems that in insets of Fig 3b the black arrow indicates the circulation dir
ection. It would be useful
to mention it in the caption.
We have implemented the suggested changes.
Reviewer #3
(Remarks to the Author):
The primary innovation in the paper "Mechanical On
-
Chip Microwave Circulator" is the first
experimental electro
-
mechanical circulator that is potentially chip
-
compatible with other cryogenic
microwave components. This is in contrast to the various demonstr
ations of opto
-
(refs 24
-
26) and
electro
-
mechanical (refs 28 & 29,
apparently 29 is now in print) isolators
, which are two port non
-
reciprocal devices, as opposed to three.
Not without good reason, non
-
reciprocal components are having a bit of a "moment"
right now in
integrated micro
-
and quantum
-
devices in the optical and RF domains, due to the limitations of the
standard technologies based on permanent magnets, as mentioned in the manuscript. Thus, this paper
opens the door to a new technological approa
ch (i.e. mechanical) to achieving non
-
reciprocity, and has
the potential to be of interest to a fairly wide audience in integrated micro
-
and quantum
-
devices in the
optical and RF domains. So I feel the topic matter and this paper in general deserves to be
published in a
broad journal. The main limitation of the paper is that the circulator's performance is extremely poor by
almost every metric compared to already proven Joseph junction
-
based RF circulators (refs. 4 & 5 are
two, but not the only examples),
and it's not at all clear how the mechanical approach could ever out
compete them. So, it deserves publication for its basic science, even if
I am very pessimistic about its technological impact.
Assuming the authors can adequately address my questions an
d comments further below, I would
generally support publication in Nature Communications.
We thank the refree for his positive comments and hope to be able to address all remaining questions in
detail below.
1) A small thing, but I generally prefer to
describe devices such as this one as "electro
-
mechanics" not
"opto
-
mechanics." Here the authors sort of use the terms interchangeably, which is not uncommon in the
field because they are so closely linked, but I wonder if it might prove confusing to other
readers.
As suggested, we have removed all instances where we used the term optomechanics and replaced it with
electromechanics.
2) Fig. 1c needs to be redrawn to make the electrical connectivity much clearer. I cannot tell at all what
is electrically con
nected to what in the nanowire device and the text didn't help me understand what I
couldn't see in the figure. In particular, I cannot tell at all where the Vdc is applying its potential. I am
very confused why "As expected, resonators 1 and 3 are tuned t
o higher frequency due to an increased
vacuum gap while resonator 2 is tuned to lower frequency." As far as I can tell in Fig. 1c, resonators 2 &
3 look identical.
We thank
the
referee for this comment.
As suggested, we have enlarged figure 1 and modified
panel c
(increased the capacitor gap sizes)
to make the circuit connections
clearer
.
For this
experiment,
we use 4 capacitors on 2 nanostrings which by design move together as one
mechanical mode of the nanobeam
(the two nanostrings are part of one silicon beam)
.
Applying a dc
voltage on the
left
side of the upper nanostring
displaces the entire nanobeam and
reduces the capacitor
gaps of both, the dc voltage capacitor on the left and the resonator 2 capacitor on
the right. Conversely,
the lower two
capacitor gaps
of resonators 1 and 3 are
increased
by
the
displacement of both
nanostring
s
.
This capacitance changes result in the
observed shifts of the
resonator frequencies.
3) In figure 1a, it looks like there are
two additional inductively coupled ports. What are these for?
The
two
high frequency ports labeled 1 and 2 are formed by shorting a coplanar waveguide center
conductor to
the
ground
plane using thin
wire
s appropriate for inductive coupling
. Port 1 uses
one
such
wire and port 2 uses
two
wires
. This design was chosen
in order to
carefully
control the extrinsic
coupling
s
and cross couplings
to each of the 3 resonator modes used
in
the experiment. The only other
connection, which is shown in the top left of pan
el 1a, is formed by two long wires that are connected to
the two sides of the dc tuning capacitor. Here we apply a static voltage for tuning the resonator
frequencies.
We have modified
the
caption to
clarify the role of the different device connections.
4
) Please state the overall footprint area of the device.
The total device area is 0.3 mm x 0.45 mm and we have added this information in the caption.
5) If the cooperativity employed in the main text figures was stated, I missed it. Similarly,
please
also
state the pump power required to achieve this cooperativity in dBm. This required power metric is helpful
in comparing this technology to others, such as the JJ devices.
We thank referee for raising this point.
We have added the cooperativities and p
ump powers as suggested.
Please also refer to
our
response to reviewer 1.
6) What is the relationship between the theory discussed at length in this paper to that described in the
theory papers referenced in refs 6, 22, & 23?
In the mentioned earlier the
ory proposals the origin of nonreciprocity relies on a coherent coupling
between the 2 resonator modes. In contrast, our experiment and theory makes use of 2 mechanical modes
to realize an effective direct interaction and realize nonreciprocity. Furthermor
e we include all cross
-
coupling terms between all the involved mechanical and resonator modes. These off resonant couplings
turn out to be essential to understand the bandwidth and the required detuning
of the drive tones from the
bare mechanical frequency
. Finally, our theory
(and experiment)
is the first to include circulator
physics
with 3 resonator and 2 mechanical modes.
W
hat is the relationship between the theory in this paper and
the theory in the JJ-based components? For
exampl
e, ref. 4 also involves parametric frequency conversion between the three port modes and two
int
ernal modes to achieve circulation. Is this approach and that one formally equivalent?
T
he underlying physics and theory of electromechanical systems is different from Josephson junction
ph
ysics with different Hamiltonians, different coupling terms and different loss mechanisms. The
par
ameter regime and approximations are different. For example the mechanical mode has finite
occ
upation limiting the added noise but it is cooled when the device is turned on. In our case in particular,
w
e use drive tones to couple two mechanical modes which in turn introduce an effective interaction
bet
ween two of the cavities – an approach that to our knowledge has not been proposed or realized in JJ
bas
ed systems.
Ha
ving said that, both the mechanical and the so far presented JJ cavity based approaches fundamentally
req
uire a dissipative bath to annihilate one of the propagation directions. Both approaches rely on
int
erfering signal paths with carefully controlled phases as imposed by external pump tones. Also, the
f
inal form of the desired scattering matrix is of course the same for any circulator, but as we pointed out
abov
e, the physics to assemble this matrix is different.
7)
I want to see not just the forward and backward scattering matrix elements, but S11, S22, & S33 as
wel
l. These input reflections are as important as the isolation for a usable device.
Figure 1 in the SI shows the performance of our device as a wavelength converter (reciprocal mode),
where we obtain excellent agreement with theory for both transmission and reflection at both ports. In
case of the isolator and circulator and having a detailed and matching theory, we distinguish between the
internal resonator loss and insertion loss due to imperfect input matching. The insertion loss is between
3.8 dB and 4.4 dB for the 3 different ports as indicated in figures 2 and 3 panel b.
We agree that a full specification of a useful circulator ideally also includes detailed information about the
reflection coefficients (in addition to the already specified impedance matching). However, the scattering
parameters we measure and fit to theory clearly proves the directionality aspect of the circulator. We feel
this is appropriate for a proof of principle circulator based on a new physical effect.
We have clarified the role and origin of the insertion loss due to finite input matching in the main text and
increased the figure and label sizes indicating the different types of losses for better visibility.
8)
Similarly, I want to see an output PSD of all three ports while the component is circulating. Again, as a
pra
ctical matter, S-parameters are not the only thing you care about in a circulator, especially an active
one.
This device employs six pump tones that are orders of magnitude stronger than the signal tones and
me
rely MHz from the signal carriers. It is critically important to know how bad all this RF leakage is.
Fig
ure 3 in the SI depicts the noise properties of the system when there is no signal circulating (measured
w
ith the spectrum analyzer with all 6 pumps on but no signal tone applied). We believe that this shows
that
there is no RF leakage from the pumps present over the relevant band (other than the added noise
sho
wn). In the presence of a weak signal tone (weak compared to the power handling capabilities) the
onl
y difference would be a narrow peak in the spectrum (depending on the chosen signal frequency and
pow
er, and the chosen resolution bandwidth of the spectrum analyzer). This peak’s magnitude is exactly
w
hat we measure when we show the S parameters in the manuscript (using a spectrum analyzer in zero
spa
n mode).
I
n the inset of figure 1 in the SI we show the signal power handling capabilities of the device used as a
w
avelength converter. For the shown S parameter measurements, we used signal powers of about -117
dB
m well below the compression point. At these small signal powers, the phase noise is negligible
compa
red to the noise induced by the (up to 6) pump tones whose relevant noise properties are shown in
f
igure 3 in the SI.
We have
added the typically used signal powers for the different experiments in the main text. We also
clari
fied the meaning of figure 3 of the SI, i.e. that it includes all unwanted noises and potential spurious
m
odes or RF leakage to be expected when the device is on (pumps are on) in the relevant section of the
S
I.
We a
gree that characterizing the noise properties of the device for higher signal powers would be
int
eresting, but we feel like it goes beyond the scope of the current manuscript and would not affect its
m
ain findings.
9)
I think it would benefit readers if the authors provided more of an honest assessment of this technol
ogy
vis
a vis other non-magnetic approaches. In particular, the JJ devices seems to out perform this one in
just abou
t every way, and it's not at all clear if this could ever change. For example, this device provided
~
10 dB relative isolation over merely ~300 Hz, while ref. 4 (the first ever demonstration) had the same
ove
r 11 MHz. This component may be tuned by 30 MHz, while that one could be tuned up to 400 MHz.
Th
is one had ~4 quanta of added noise, while that one had 0.5 (quantum limited). This one requires six
RF pump
s, that one 3. Presumably the pump power required here is again orders of magnitude greater
tha
n in ref. 4, because the nonlinearity is so much weaker. If I had to guess, this mechanical technology
mi
ght only be able to outperform the JJ ones in 1 dB compression point, again because the nonlinearity is
so
much weaker.
The referee raises some important points by comparing JJ devices to our mechanical version of a chip
scale circulator. He/she is right that it will be difficult for mechanical systems to outperform JJ devices in
terms of bandwidth. But in our opinions, it is too early to draw a definitive conclusion because in the end
the bandwidth mainly depends on how strongly the system can be coupled to the dissipative bath.
In terms of added noise the mechanical systems need to be cooled to thermal occupations close to the
ground state. The final occupancy for the reported device already reached as low as 0.6 quanta (for a
single and strong cooling tone – the second mechanical mode reached an occupancy as low as 2 quanta).
We are convinced that improved fabrication and design will lower the total added noise in the future to
reach similar levels as JJ devices.
While our circulator required 6 pump tones because we work with 2 mechanical modes, improved designs
with predictable direct resonator coupling will only require 3 pump tones.
While it might be challenging to catch up with existing technology on all fronts, we also see a number of
unique advantages of mechanical systems compared to JJ technology:
-
Me
chanics is insensitive to magnetic field noise and offsets.
-
As
pointed out by the referee, the dynamic range can be higher (useful for example for high
pow
er dispersive qubit readout without a parametric amplifier). For the reported device operated
as
a wavelength converter no power saturation occurs for up 10^4 cavity photons or about -90
dB
m of signal power.
-
Mechanical elements are well
-
localized objects where parasitic coupling across circuits on the
same chip is reduced compared to electromagnetic modes.
-
Devices based on mechanical oscillators have the p
otential for hybrid microwave
and optical
signal processing, i
n particular non
-
reciprocity between microwave and optical propagating
fields.
We have added a concluding paragraph outlining the challenges and potential of
our
results in particular
in compari
son with Josephson junction devices.
As for the proposed application of superconducting qubit readout, the bandwidth of those signals are
measured in MHz, and carriers can easily vary by 100 MHz without a very well controlled process. Even
with its better
parameters, the limitations of ref. 4 have yielded little actual technological impact so far
for this application either. I want to reiterate that publishable work just has to be innovative, rather than
technologically competitive, but the authors can only
help the field by comparing it to other technologies
and offering more guidance on where improvements will be best made.
We agree that the path to actual impactful applications can be a long one. Our main goal was to show
important new physics and demonstrate what state of the art electromechanics can
do today
.
This has
been achieved in a new SOI
platform that is compatible
with
both qubits
and silicon photonics. In the next
years we will work on making our circuits smaller, more integrated,
more reliable and more useful.
REVIEWERS' COMMENTS:
Reviewer #1 (Remarks to the Author):
I am very happy with the revised manuscript as the authors have carefully addressed all the
comments and suggestions raised in the reports. I have no further questions on it and therefore, I
recommend it for consideration of publication in Nature Communica
tions. No further review is
necessary.
Reviewer #2 (Remarks to the Author):
My concerns are addressed. I recommend for publication.
Reviewer #3 (Remarks to the Author):
This is the second time I have reviewed the manuscript "Mechanical on
-chip mi
crowave circulator."
I thank the authors for their in
-
depth reply and responsiveness to my and the other referee
comments.
I think the paper is suitable for publication as long as they remove the last statement "Direct
integration with superconducting qu
bits should allow for on
-chip single photon routing..."
This component is orders upon orders upon orders of magnitude away from being suitable for this
application. The -
70 dBm CW pump tones mere MHz from the signal frequency will strongly drive
any circ
uit QED readout cavity and completely blow away the qubit. Moreover, the 600 Hz
bandwidth is more than 10^3 too restrictive for any cQED
-
appropriate signal routing. In contrast,
the JJ
-based circulators have less of a problem with this application because
the pumps are much,
much weaker, are GHz detuned, and have ~10s MHz of bandwidth. Readers (or the authors)
should not be encouraged to integrate this device with a superconducting qubit.